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Parity-time对称性对电注入半导体激光器的模式控制

王学友 王宇飞 郑婉华

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Parity-time对称性对电注入半导体激光器的模式控制

王学友, 王宇飞, 郑婉华

Mode control of electrically injected semiconductor laser with parity-time symmetry

Wang Xue-You, Wang Yu-Fei, Zheng Wan-Hua
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  • 非厄米的描述对于开放系统有重要意义, 满足parity-time对称性的哈密顿量, 其参数在一定范围内可以使能量具有实的本征值. 本文通过模拟, 研究了损耗大小以及结构对称性对条形波导中的parity-time对称性的影响, 并通过实验发现了电注入条件下由parity-time对称破缺导致的脊条波导模式间隔加倍、模式数减半的现象.
    The non-Hermitian description is of great significance for open systems, and the Hamiltonian which satisfies parity-time symmetry can make the energy have real eigenvalue within a certain range. The properties of parity-time symmetry have bright application prospects in optical systems. For semiconductor lasers, the parity-time symmetry can be constructed by adjusting the level of electrical injection to help achieve better mode control. Electric injection is easier to realize than optical pump when the device size is small and the structure is complex. Therefore, we hope to analyze the characteristics of the laser that satisfies the parity-time symmetry condition under the condition of electric injection. In this paper, we simulate the effects of different set loss values on parity-time symmetry. It is found that with the increase of set loss value, the imaginary part of the refractive index of the gain cavity corresponding to the parity-time symmetry breaking point so-called exceptional point will decrease, and the imaginary part of the characteristic frequency corresponding to the exceptional point will also decrease. We also simulate the effect of structural size ratio of gain region and loss region on parity-time symmetry. On condition that the total cavity length and the imaginary part of the refractive index of the loss region remain unchanged, as the gain cavity becomes longer and the loss cavity becomes shorter, the imaginary part of the refractive index of the gain cavity corresponding to the exceptional point will increase, and the imaginary part of the characteristic frequency corresponding to the exceptional point will also increase. And we qualitatively explain the above phenomenon through the coupled mode equations. Through experiments, metal organic chemical vapor deposition (MOCVD) and standard lithography techniques are used to fabricate asymmetric ridge lasers. Under thermoelectric cooler (TEC) refrigeration and by controlling the injection level of the gain area, the doubled mode spacing and halved mode number of ridge waveguide are found for the first time due to the parity-time symmetry breaking under the condition of electric injection. We believe that the study of parity-time symmetry in ridge laser under the condition of electric injection will be of great help in implementing the mode control.
      通信作者: 郑婉华, whzheng@semi.ac.cn
    • 基金项目: 国家重点研发计划(批准号: 2016YFB0401804, 2016YFB0401003, 2016YFA0301102)和国家自然科学基金(批准号: 91850206, 61535013)资助的课题
      Corresponding author: Zheng Wan-Hua, whzheng@semi.ac.cn
    • Funds: Project supported by the National Key Research and Development Program of China (Grant Nos. 2016YFB0401804, 2016YFB0401003, 2016YFA0301102) and the National Natural Science Foundation of China (Grant Nos. 91850206, 61535013)
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    Gamow G 1928 Z. Für Phys. 51 204Google Scholar

    [2]

    Dirac P A M, F R S 1942 Proceedings A 180 1

    [3]

    Feshbach H, Weisskopf V F, Porter C E 1954 Nucl React 96 227

    [4]

    Brower R C, Furman M A, Moshe M 1978 Phys. Lett. B 76 213Google Scholar

    [5]

    Denham S A, Harms B C, Jones S T 1981 Nucl. Phys. B 188 155Google Scholar

    [6]

    Andrianov A A 1982 Ann. Phys.-New York 140 82Google Scholar

    [7]

    Hollowood T J 1992 Nucl. Phys. B 384 523Google Scholar

    [8]

    Scholtz F G, Geyer H B, Hahne F J W 1992 Ann. Phys.-New York 213 74Google Scholar

    [9]

    Caliceti E, Graffi S, Maioli M 1980 Commun. Math. Phys. 75 51Google Scholar

    [10]

    Bender C M, Boettcher S 1998 Phys. Rev. Lett. 80 5243Google Scholar

    [11]

    Bender C M, Dunne G V, Meisinger P N 1998 Phys. Lett. A 252 272

    [12]

    Dorey P, Dunning C, Roberto T 2001 J. Phys. A: Gen. Phys. 34 L391Google Scholar

    [13]

    Ruschhaupt A, Delgado F, Muga J G 2017 J. Phys. A: Gen. Phys. 38 L171

    [14]

    Brandstetter M, Liertzer M, Deutsch C, Klang P, Schöberl J, Türeci H E, Strasser G, Unterrainer K, Rotter S 2014 Nat. Commun. 5 4034Google Scholar

    [15]

    Gao Z, Fryslie S T M, Thompson B J, Carney P S, Choquette K D 2017 Optica 4 323Google Scholar

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    Guo A, Salamo G J, Duchesne D, Morandotti R, Volatierravat M, Aimez V, Siviloglou G A, Christodoulides D N 2009 Phys. Rev. Lett. 103 093902Google Scholar

    [17]

    Makris K G, El-Ganainy R, Christodoulides D N, Musslimani Z H 2008 Phys. Rev. Lett. 100 103904Google Scholar

    [18]

    Zhen B, Hsu C W, Igarashi Y, Lu L, Kaminer I, Pick A, Chua S L, Joannopoulos J D, Marin S 2015 Nature 525 354Google Scholar

    [19]

    Doppler J, Mailybaev A A, Böhm J, Kuhl U, Girschik A, Libisch F, Milburn T J, Rabl P, Moiseyev N, Rotter S 2016 Nature 537 76Google Scholar

    [20]

    Xu H, Mason D, Jiang L, Harris J G E 2016 Nature 537 80Google Scholar

    [21]

    Gu Z, Zhang N, Lyu Q, Li M, Xiao S, Song Q 2016 Laser Photonics Rev. 10 588Google Scholar

    [22]

    Zhang N, Gu Z, Wang K, Li M, Ge L, Xiao S, Song Q 2017 Laser Photonics Rev. 11 1700052Google Scholar

    [23]

    Zhao S, Qi A, Wang M, Qu H, Lin Y, Dong F, Zheng W 2018 Opt. Express 26 3518Google Scholar

    [24]

    Coldren L A 2012 Diode Lasers and Photonic Integrated Circuits (America: John Wiley & Sons) pp335–391

    [25]

    Rüter C E, Makris K G, El-Ganainy R, Christodoulides D N, Segev M, Kip D 2010 Nat. Phys. 6 192Google Scholar

    [26]

    Hodaei H, Hassan A U, Wittek S, Garcia-Gracia H, El-Ganainy R, Christodoulides D N, Khajavikhan M 2017 Nature 548 187Google Scholar

  • 图 1  外延片结构图

    Fig. 1.  Epitaxy structure of wafers.

    图 2  器件结构图, 其中黄色部分为增益区, 蓝色部分为损耗区

    Fig. 2.  Device structure diagram, the yellow part is the gain region and the blue part is the loss region.

    图 3  条型波导模拟结构图

    Fig. 3.  Simulation structure of stripe waveguide.

    图 4  折射率虚部为${n_{{\rm{Ir}}}} = - 0.01$${n_{{\rm{Ir}}}} = - 0.05$时, 波长与${n_{{\rm{Il}}}}$的关系图

    Fig. 4.  Relationship between wavelength and ${n_{{\rm{Il}}}}$ when ${n_{{\rm{Ir}}}} = - 0.01$ and ${n_{{\rm{Ir}}}} = - 0.05$.

    图 5  折射率虚部为nIr = –0.01以及nIr = –0.05时, 特征频率虚部与${n_{{\rm{Il}}}}$的关系图

    Fig. 5.  Relationship between the imaginary part of the characteristic frequency and ${n_{{\rm{Il}}}}$ when ${n_{{\rm{Ir}}}} = - 0.01$ and ${n_{{\rm{Ir}}}} = - 0.05$.

    图 6  增益区和损耗区长度比为5∶5, 7∶3以及8∶2时的结构图

    Fig. 6.  Simulation structure of ridged waveguide when length ratio of gain region and loss region is 5∶5, 7∶3, and 8∶2.

    图 8  长度比为5∶5, 7∶3以及8∶2时, 特征频率虚部与${n_{{\rm{Il}}}}$的关系图

    Fig. 8.  Relationship between the imaginary part of the characteristic frequency and ${n_{{\rm{Il}}}}$ when the length ratio is 5∶5, 7∶3, and 8∶2.

    图 7  长度比为5∶5, 7∶3以及8∶2时, 波长与${n_{{\rm{Il}}}}$的关系图

    Fig. 7.  Relationship between wavelength and ${n_{{\rm{Il}}}}$ when the length ratio is 5∶5, 7∶3, and 8∶2.

    图 9  腔模强度与波长关系 (a)注入电流为100 mA; (b)注入电流分别为310 mA(黑线)、320 mA(红线)以及330 mA(蓝线)

    Fig. 9.  Relationship between the normalized intensity and wavelength of cavity modes: (a) The injection current is 100 mA; (b) the injection current is 310 mA (black line), 320 mA (red line) and 330 mA (blue line), respectively.

  • [1]

    Gamow G 1928 Z. Für Phys. 51 204Google Scholar

    [2]

    Dirac P A M, F R S 1942 Proceedings A 180 1

    [3]

    Feshbach H, Weisskopf V F, Porter C E 1954 Nucl React 96 227

    [4]

    Brower R C, Furman M A, Moshe M 1978 Phys. Lett. B 76 213Google Scholar

    [5]

    Denham S A, Harms B C, Jones S T 1981 Nucl. Phys. B 188 155Google Scholar

    [6]

    Andrianov A A 1982 Ann. Phys.-New York 140 82Google Scholar

    [7]

    Hollowood T J 1992 Nucl. Phys. B 384 523Google Scholar

    [8]

    Scholtz F G, Geyer H B, Hahne F J W 1992 Ann. Phys.-New York 213 74Google Scholar

    [9]

    Caliceti E, Graffi S, Maioli M 1980 Commun. Math. Phys. 75 51Google Scholar

    [10]

    Bender C M, Boettcher S 1998 Phys. Rev. Lett. 80 5243Google Scholar

    [11]

    Bender C M, Dunne G V, Meisinger P N 1998 Phys. Lett. A 252 272

    [12]

    Dorey P, Dunning C, Roberto T 2001 J. Phys. A: Gen. Phys. 34 L391Google Scholar

    [13]

    Ruschhaupt A, Delgado F, Muga J G 2017 J. Phys. A: Gen. Phys. 38 L171

    [14]

    Brandstetter M, Liertzer M, Deutsch C, Klang P, Schöberl J, Türeci H E, Strasser G, Unterrainer K, Rotter S 2014 Nat. Commun. 5 4034Google Scholar

    [15]

    Gao Z, Fryslie S T M, Thompson B J, Carney P S, Choquette K D 2017 Optica 4 323Google Scholar

    [16]

    Guo A, Salamo G J, Duchesne D, Morandotti R, Volatierravat M, Aimez V, Siviloglou G A, Christodoulides D N 2009 Phys. Rev. Lett. 103 093902Google Scholar

    [17]

    Makris K G, El-Ganainy R, Christodoulides D N, Musslimani Z H 2008 Phys. Rev. Lett. 100 103904Google Scholar

    [18]

    Zhen B, Hsu C W, Igarashi Y, Lu L, Kaminer I, Pick A, Chua S L, Joannopoulos J D, Marin S 2015 Nature 525 354Google Scholar

    [19]

    Doppler J, Mailybaev A A, Böhm J, Kuhl U, Girschik A, Libisch F, Milburn T J, Rabl P, Moiseyev N, Rotter S 2016 Nature 537 76Google Scholar

    [20]

    Xu H, Mason D, Jiang L, Harris J G E 2016 Nature 537 80Google Scholar

    [21]

    Gu Z, Zhang N, Lyu Q, Li M, Xiao S, Song Q 2016 Laser Photonics Rev. 10 588Google Scholar

    [22]

    Zhang N, Gu Z, Wang K, Li M, Ge L, Xiao S, Song Q 2017 Laser Photonics Rev. 11 1700052Google Scholar

    [23]

    Zhao S, Qi A, Wang M, Qu H, Lin Y, Dong F, Zheng W 2018 Opt. Express 26 3518Google Scholar

    [24]

    Coldren L A 2012 Diode Lasers and Photonic Integrated Circuits (America: John Wiley & Sons) pp335–391

    [25]

    Rüter C E, Makris K G, El-Ganainy R, Christodoulides D N, Segev M, Kip D 2010 Nat. Phys. 6 192Google Scholar

    [26]

    Hodaei H, Hassan A U, Wittek S, Garcia-Gracia H, El-Ganainy R, Christodoulides D N, Khajavikhan M 2017 Nature 548 187Google Scholar

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出版历程
  • 收稿日期:  2019-09-06
  • 修回日期:  2019-10-15
  • 上网日期:  2020-01-01
  • 刊出日期:  2020-01-20

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